Quantum machine learning with adaptive linear optics

We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements. We then challenge these quantum algorithms by deriving classical simulation algorithms for the tasks of output probability estimation and overlap estimation. We obtain different classical simulability regimes for these two computational tasks in terms of the number of adaptive measurements and input photons. In both cases, our results set explicit limits to the range of parameters for which a quantum advantage can be envisaged with adaptive linear optics compared to classical machine learning algorithms: we show that the number of input photons and the number of adaptive measurements cannot be simultaneously small compared to the number of modes. Interestingly, our analysis leaves open the possibility of a near-term quantum advantage with a single adaptive measurement.Comment: 16 + 5 pages, presented at AQIS2020, accepted in Quantu

Corrected Bell and Noncontextuality Inequalities for Realistic Experiments

Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism. The former can be justified by the empirical property of non-signalling or non-disturbance, and the latter by the empirical property of measurement sharpness. However, in realistic experiments neither empirical property holds exactly, which leads to possible objections to contextuality as a form of nonclassicality, and potential vulnerabilities for supposed quantum advantages. We introduce measures to quantify both properties, and introduce quantified relaxations of the corresponding assumptions. We prove the continuity of a known measure of contextuality, the contextual fraction, which ensures its robustness to noise. We then bound the extent to which these relaxations can account for contextuality, via corrections terms to the contextual fraction (or to any noncontextuality inequality), culminating in a notion of genuine contextuality, which is robust to experimental imperfections. We then show that our result is general enough to apply or relate to a variety of established results and experimental setups.Comment: 20 pages + 14 pages of appendices, 3 figure

Certifying dimension of quantum systems by sequential projective measurements

This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability

High photon-loss threshold quantum computing using GHZ-state measurements

We propose fault-tolerant architectures based on performing projective measurements in the Greenberger-Horne-Zeilinger (GHZ) basis on constant-sized, entangled resource states. We present linear-optical constructions of the architectures, where the GHZ-state measurements are encoded to suppress the errors induced by photon loss and the probabilistic nature of linear optics. Simulations of our constructions demonstrate high single-photon loss thresholds compared to the state-of-the-art linear-optical architecture realized with encoded two-qubit fusion measurements performed on constant-sized resource states. We believe this result shows a resource-efficient path to achieving photonic fault-tolerant quantum computing

Etude de tests du caractère quantique de systèmes de dimension supérieur à deux dans des conditions réalistes

The subject of this thesis is a study of tests of the quantum features of systems of dimension greater than two under realistic conditions. Non-locality is one of the quantum properties used in protocols in the field of quantum communications. The study on the effects of the decoherence (models ofrealistic conditions) address the issue of the conservation of non-locality in practice. Contextuality is another fundamental quantum property with a potential power in quantum information processing. A contextuality test has been developed for all dimensions of quantum systems greater than two. An experiment that considers the experimental issues of contextuality tests is also proposed.Le sujet de cette thèse est une étude de tests du caractère quantique des systèmes de dimension supérieure à deux dans des conditions réalistes. La non-localité est une des propriétés quantiques utile pour des protocoles du domaine des communications quantiques. L’étude réalisée sur les effets de la décohérence (modèles de conditions réalistes) permet de rendre compte des moyens à mettre en oeuvre afin d’optimiser la conservation de la non-localité en pratique. La contextualité est une autre propriété quantique fondamentale avec un potentiel dans le domaine de traitement d’information quantique. Un test de contextualité a été développé pour toutes les dimensions de systèmes quantiques supérieures à deux. Une expérience prenant en compte les enjeux expérimentaux des tests de contextualité est aussi proposée

Study of access of quantum features of high dimensional systems under realistic conditions

Le sujet de cette thèse est une étude de tests du caractère quantique des systèmes de dimension supérieure à deux dans des conditions réalistes. La non-localité est une des propriétés quantiques utile pour des protocoles du domaine des communications quantiques. L’étude réalisée sur les effets de la décohérence (modèles de conditions réalistes) permet de rendre compte des moyens à mettre en oeuvre afin d’optimiser la conservation de la non-localité en pratique. La contextualité est une autre propriété quantique fondamentale avec un potentiel dans le domaine de traitement d’information quantique. Un test de contextualité a été développé pour toutes les dimensions de systèmes quantiques supérieures à deux. Une expérience prenant en compte les enjeux expérimentaux des tests de contextualité est aussi proposée.The subject of this thesis is a study of tests of the quantum features of systems of dimension greater than two under realistic conditions. Non-locality is one of the quantum properties used in protocols in the field of quantum communications. The study on the effects of the decoherence (models ofrealistic conditions) address the issue of the conservation of non-locality in practice. Contextuality is another fundamental quantum property with a potential power in quantum information processing. A contextuality test has been developed for all dimensions of quantum systems greater than two. An experiment that considers the experimental issues of contextuality tests is also proposed

Decoherence Effects on the Non-locality of Symmetric States

International audience<p>In this paper we analyze criteria for robustness of non-locality of symmetric states. We develop ourresearch using the recently developed extended Hardy’s paradox non-locality test. We investigatethe case of symmetric states, we show that for high numbers of qubits the non-locality of W statecan tolerate high degree of noise. We also demonstrate that the choice of the bases is, in particularcases, an important criterion for robustness independently from the bases which give high violation.We also apply our techniques to a discrimination of entanglement class.</p